MATH 122-03, Calculus II, Spring 2009

Abstract

We will cover the following material from the text. Chapter 5, Sections 4 – 8: Review of the fundamental theorem of calculus and integration by substitution, both of which you should have seen in Calculus I. Numerical integration. The natural logarithm as an integral. Integrals involving inverse trigonometric functions. Chapter 6, Sections 1 – 4: Differential equations. Graphical and numerical methods, such as slope fields and Euler’s method. Application to growth and decay, including the logistic equation. Chapter 7, Sections 1 – 7: Areas, lengths, and volumes. Moments, centers of mass, and centroids. Applications to work and fluid statics. Chapter 8, Sections 1 – 5, 7, and 8: Techniques for integration, including integration by parts, trigonometric integrals and substitution, and partial fractions. L’Hopital’s rule. Improper integrals. Chapter 9, Sections 1 – 10: Sequences. Series. Tests for convergence, including the integral, p-, comparison, alternating series, ratio, and root tests. Taylor polynomials. Power series and their role in describing functions. Taylor and Maclaurin series.